Equation apparatus

ABSTRACT

Equation apparatus has at least first, second, and third number dials which are manually movable to indicate particular digits. An output indicator is connected to all three of the dials, to signal when an equation is satisfied by the digits on the dials. Each of the dials has a manual knob. A one-way drive interconnects these parts to the output indicator so that each manually movable structure and number dial can be individually turned independent of the other number dials.

1 Oct. 10,1972

United States Patent Stewart [54] EQUATION APPARATUS FOREIGN PATENTS ORAPPLICATIONS Inventor: Larry Slewart, 7104 Jordan 650,205 2/1951GreatBritain.......... ..35/3lR Ave., Apt. 4, Canoga Park, Calif.

91304 Primary Examiner-Wm. H. Grieb 22 Filed: May 17 971 Attorney-AllanM. Shapiro [21] Appl. No.: 143,913

[57] ABSTRACT Equation apparatus has at least first, second, and thirdnumber dials which are manually movable to indicate particular digits.An output indicator is connected to [52] US. Cl. A [51] Int. 19/02 [58]Field ofSearch.........3S/31 R, 31 A, 31 B, 31 C, 35/30, 9 R

all three of the dials, to signal when an equation is satisfied by thedigits on the dials. Each of the dials has a manual knob. A one-waydrive interconnects these parts to the output indicator so that each[56] References Cited UNITED STATES PATENTS manually movable structureand number dial can be individually turned independent of the othernumber 1,948,712 2/1934 Homung................35/31 C X dials 2,618,86811/1952 Medlock....................35/3l A 2,643,467

26 Claims, 12 Drawing Figures 6/1953 Goodwin ...................35/31 APKTENTEDHM 10 m2 SHEET 1 [IF 3 [lllllllll INVENTOR. L mey (Z. STEM/A27"EQUATION APPARATUS BACKGROUND OF THE INVENTION 1. Field Of The InventionThis invention is directed to an equation apparatus which acts as ateaching device to show the user when a mathematical equation is solved.It is particularly useful as a teaching device for single digit additionand subtraction problems.

2. Description Of The Prior Art The most common teaching means forteaching elementary arithmetic, particularly addition and subtraction,comprises the arrangement of numbers in tabular form so that the sum isindicated at an intersection. These tabular devices are widely known asaddition tables, and appear to have been used in teaching arithmeticvirtually since its inception.

Another prior art effort at providing teaching equipment for problems inaddition and subtraction has been the balance scale where theapplication of weights to a scale arm results in its deflection, toindicate a result or to indicate that equality has not beenaccomplished. These devices are useful, but require loose weights, orthe like, which can be placed upon the scale or moved so that moment armequality is established to result in scale balance.

Few devices which have mechanically interconnected structures have beenproduced. One of them is merely a modernization of the old tabular form,which brings up columns beneath a visible window upon adjustment.Another employs levers to produce a sum, with a readout being related tothe lever position. Another prior art device relates multiplication tothe relative rotation of interengaged gears. Different gear diametersresult in the indication of different equation situations. However, lessthan a full turn of such gears causes difficulties in interpretation ofresults.

The prior art, thus, leaves much to be desired, for there is no adequateteaching device which is economic of manufacture, and easy to use sothat it presents an interesting challenge to the young students who arelearning arithmetic, for these students must have a device which issimple of operation, reliable and accurate in results. Furthermore, theprior devices have not conveniently indicated both addition andsubtraction situations, so there is much need for teaching devices ofsuch nature.

SUMMARY OF THE INVENTION In order to aid in the understanding of thisinvention, it can be stated in essentially summary form that it isdirected to an equation apparatus. The equation apparatus has at leastthree number wheels, and has a manually movable structure connected tomove the number wheels. The wheels are moved to a position whereequality is accomplished in the equation.

First, second, and third shafts 18, and 22 respectively carry mainoperating knobs 24, 26 and 28 secured to their front ends. Carriers 30,32 and 34 are respectively secured on the shafts. Carriers 30, 32 and 34are identical and thus only carrier 30 will be described. Fixed to theforward end of carrier 30, that is, closest to the cover plate 12 andfirst knob 24, is a rachet wheel 36. The corresponding ratchet wheeldriven by third main operating knob 28 is indicated at 38 in FIG. 3. Thefirst carrier 30 is secured to shaft 18 LII to rotate therewith, and isin the form of a disc. Secured to the disc and facing inwardly are pawls40 and 42 (see FIG. 3).

Positioned within the engagement of pawls 40 and 42 is ratchet wheel 44.The pawls and the ratchet wheel are arranged so that, when knob 24 andfirst shaft 18 are rotated in the clockwise direction, as seen in FIGS.1 and 4, such clockwise rotation of shaft 18 drives ratchet wheel 44 inthe clockwise direction. Ratchet wheel 44 is mounted upon sleeve 46which is freely rotatable on the exterior of shaft 18. The forward endof sleeve 46 carries pinion 48 secured thereto for rotation therewith.By this construction, clockwise rotation of knob 24 rotates shaft 18 inthe clockwise direction, and similarly rotates first carrier 30 and itspawls 40 and 42 in the clockwise direction. Such rotation causes thepawls to drive ratchet wheel 44, sleeve 46 and pinion 48 in theclockwise direction. However, counter-clockwise rotation of knob 24would not rotate pinion 48 because of the non-drive of the pawls in thisdirection. Similarly, clockwise rotation of pinion 48 would not causerotation of first carrier 30.

Support plate 14 is preferably laminated, of three layers, to providepockets therein. As illustrated in FIG. 2, support plate 14 hassubstantially continuous front and rear layers, but the middle layerthereof has larger holes for the reception of gears, as is illustratedin FIG. 4. The rear ends of shafts I8, 20 and 22 respectively carryfirst, second and third pinions 48, 50 and 52. As indicated with respectto first pinion 48, these pinions are not directly driven by the shaftson which they are supported, but are respectively driven throughcarriers 30, 32 and 34 so that the pinions rotate in a clockwisedirection when their respective main operating knobs are rotated in theclockwise direction.

Idler 54 is mounted in support plate 14 and is in geartooth engagementwith both pinions 48 and 50. Idler 56 is in gear-tooth engagementwithpinion 52, and engages with indicator carrier gear 58. Indicatorcarrier gear 58 is also in gear-tooth engagement with pinion 50. Thethree pinions, the two idlers, and the indicator carrier gear are inconstant mesh so that, when one rotates, the others must rotate. Thedirection of rotation of all of the gears is shown by arrows in FIG. 4,when pinion 48 or pinion 50 is rotated in the clockwise direction; eachof the direction arrows of rotation would be reversed when pinion 52 isrotated in the clockwise direction.

Indicator carrier gear 58 is connected to drive indicator support gear60, and mounted on top of the indicator support gear 60 is indicatorgear 62. The indicator gear 62 may carry a transverse bar 64 thereonwhich preferably has characteristic configurations on the ends toindicate the difference between one orientation of the indicator gear62, as compared to an orientation 180 therefrom, i.e., upside-down.FIGS. 66 and 68 are ornamental and attractive and satisfy this purpose.

Indicator gear 62 is loosely seated on the top of indicator support gear60, but is guided to remain in the correct position by guides 70 and 72.An additional set of guides 70 and 72' are provided on the oppositeside, as seen in FIG. 4, for purposes hereinafter described.

First, second and third number dials or wheels 74, 76 and 78 arerespectively mounted for rotation about shafts 18, 20 and 22, and arepositioned directly behind cover plate 12. The number wheels each carrythe 10 digits, i.e., to 9 inclusive, equally spaced therearound, to berespectively visible through windows 80, 82 and 84 in front plate 12.Adjustment knobs 86, 88 and 90 are also rotatably mounted on shafts 18,20 and 22, and the adjustment knobs are connected to the respectivenumber wheels by means of sleeves extending through the front plate. Oneof these sleeves is indicated at 92 in FIGS. 2 and 6. Thus, manualengagement and rotation in either direction of any of the adjustmentknobs causes corresponding rotation of the number wheel connectedthereto.

The rear of each of the number wheels has a pawl carrier thereon. Thepawl carrier on the rear of number wheel 74 is shown at 94, as carryingpawl 96. Similarly, the pawl carrier on the rear of number wheel 78 isindicated at 98 and its pawl is shown at 100, in FIGS. 2 and 3. Thesepawls engage upon the ratchet wheels at the front of carriers 30, 32 and34, respectively, and are oriented in such a manner that, when theadjustment knobs 86 through 90 are individually manually rotated in theclockwise direction, only the connected number wheel rotates. However,when one of the ratchet wheels mounted on the front of pawl carriers 30through 34 is rotated in the clockwise direction, engagement by the pawlon the number wheel causes clockwise rotation of the number wheel.

The gears described as driving the indicator gear 62 and indicator bar64 are illustrative of the positive drive means. Other types of positivedrive means could be employed instead of the gears, idlers and pinions.One example of an economic and positive drive means of suitablecharacter is the beadchain, with special positively engaging beadchainsprockets.

In operation, the equation apparatus 10 is preferably placed upon ahorizontal surface in the orientation illustrated in FIG. 7a. Indicatorgear 62 with its bar is placed on the top of the equation apparatus,with the bar in a horizontal position. The numbers on number wheels 74through 78 which are visible through windows 80 through 84 are set tozero by respectively grasping the adjustment knobs 86 through 90 andindividually turning these knobs in the clockwise direction until a zeroappears in each of the windows. Such clockwise motion of the adjustmentknobs results in turning of the number wheels without any other activityin the equation apparatus, because the pawl on the rear of the numberwheel ratchets around its ratchet wheel without driving. For example,pawl 96 ratchets around ratchet wheel 36 without driving ratchet wheel36.

The first step in employing the equation apparatus to test a set ofnumbers to see if they fit the equation is to first turn one of the mainoperating knobs such as knob 24 in the clockwise direction until theselected number appears in window 80. In FIG. 7a, the number 2 is theselected number. With the turning of the main operating knob 24, carrier30 turns in the clockwise direction, which causes drive of the numberwheel 74, in this case, until the number 2 is reached, and causes driveof pinion 48 through pawl 40 and ratchet wheel 44. For this rotation ofpinion 48, all the gears in support plate I4 turn in the directionsindicated by the arrows. The rotation of indicator gear 62 tilts the bar64, as illustrated in FIG. 7a. This rotation of the gears in supportplate 14 does not turn number wheel 76, because the pawl in pawl carrier32 does not drive when pinion 50 is driven in the clockwise direction.Similarly, while pinion 52 drives pawl carrier 34, because it isrotating in the counter-clockwise direction, and thus knob 28 rotates inthe counterclockwise direction, as indicated in FIG. 7a, the numberwheel 78 does not turn because this is the free turning direction ofpawl with respect to ratchet wheel 38. Thus, the originally set zeros inwindows 82 and 84 remain set at zero.

FIG. 7b illustrates the next step in operation, where main operatingknob 26 is turned in the clockwise direction to bring up the selectednumber in window 82. The selected number is the number I as seen in FIG.7b. As the operating knob 26 and the number wheel turn in the clockwisedirection, pinion 50 is also driven in the clockwise direction by thesame mechanization as previously described with respect to pinion 48.This drives indicator gear 62 and its bar 64 farther in the clockwisedirection, as is indicated in FIG. 7b. I

As the final step in determining whether or not the selected numbers fitthe equation, main operating knob 28 is turned in the clockwisedirection until the selected number shows through window 84. In thiscase, the number 3 is selected. Rotation of the main operating knob inthe clockwise direction causes clockwise rotation of pinion 52. Suchrotation causes rotation of all the gears illustrated in FIG. 4 in thedirection opposite to the arrows shown therein. Rotation occurs untilthe selected number shows in window 84. If the equation is satisfied,rotation of gear 60 in the clockwise direction caused by clockwiserotation of pinion 52 is the same in amount as the originalcounterclockwise rotation thereof caused by driving through pinions 48and 50. In the present case, the equation tested is an addition equationillustrated by the plus sign between windows 80 and 82 and the equalssign between windows 82 and 84 on the upper half of cover plate 12, asseen in FIGS. 1 and 7.

The importance of having significant upper and lower sides on bar 64 isseen when the two numerals for addition add up to 10 or more. Forexample, when 5 plus 5 are dialed into the main operating knobs 24 and26, indicator gear 62 and its bar 64 rotate 5" plus 5 equals 0" (butread as 10 because only the first decade is shown in the number wheels)is correct, the factor of 10 involved is indicated by the bar 64 beingupside down. The bar is righted to its correct position by a fullrevolution of main operating knob 28, which rotates the number wheel 78a full decade to more correctly indicate the propriety of the equation.

The equation apparatus 10 can be employed in two basic ways, employingthe addition equation. In one manner of use, numbers can be selected foreach of the three windows and the horizontal or tilted condition of bar64 states whether or not these values satisfy the equation. In the otheruse, numbers can be selected for any two of the windows, and the numberin the third window can be continuously changed until the horizontalcondition of bar 64 indicates that the equation is satisfied, and thusthe value for this equation satisfaction is indicated in the thirdwindow.

The same equation apparatus can be turned over on its supporting surfaceto show windows 102, 104 and 106 through which the number wheels 74, 76and 78 are respectively visible (see FIG. 8a. Windows 102 and 104 areseparated by an equals sign, while windows 104 and 106 are separated bya minus sign. When the indicator gear 62 with its bar 64 is placed ontop of the indicator support gear 60, when the equation apparatus 10 isin this orientation, the apparatus is useful for solving subtractionequations. Operation is similar to that previously described. First, thenumber wheels are set to zero as by clockwise rotation of the adjustmentknobs, and indicator bar 64 is set in the level position.

As the first step in employing equation apparatus 10 as a subtractingdevice, main operating knob 28 is turned in the clockwise direction to aselected number on the number wheel 78 visible through window 106. Inthis case, the number is the numeral 2, as illustrated in FIG. 8a.During this rotation of main operating knob 28, the bar 64 rocks asindicated, and knobs 24 and 26 rotate in the counter-clockwisedirection, without rotation of their respective number wheels.

Next, main operating knob 26 is turned in the clockwise direction, untilthe number wheel 76 shows a selected number through window 104. In thiscase, the selected number is l as indicated in FIG. 8b. During thisrotation, main operating knob 28 rotates in the counter-clockwisedirection, but the number wheels 74 and 78 do not move. The bar 64 rockspartway back to its horizontal position. Finally, knob 24 is rotated inthe clockwise direction until the selected number shows through window102 and number wheel 74. In this case, the number I is selected, asshown in FIG. 80. This satisfies the subtraction equation, as indicatedby the horizontal condition of bar 64. In subtraction, as well as inaddition, the equation apparatus can be employed either to determinewhether or not three selected numbers satisfy the equation, or todetermine the third number which satisfies the equation, when two arepreselected.

Indicator carrier gear 58, indicator support gear 60, indicator gear 62,and bar 64 provide a means for indicating when the indicator carriergear 58 has returned to its original angular position. The preferredembodiment illustrated is particularly satisfactory because the equationapparatus 10 is intended as a teaching device for children, and such anexternal bar 64 tends to correlate the balancing" concepts involved inboth teeter'totters and equations. However, other indicator means, suchas an electric switch which is closed when the indicator carrier gear 58returns to its initial position, can be employed to signal when thisevent has occurred.

The equation apparatus 10 is such that it is economic of construction,and yet is accurate. Synthetic polymer composition materials can be usedfor most of the parts, and as an added feature for attention-gettingemployment by a child, many of the components can be made of transparentsynthetic polymer composition material so that the moving parts can beobserved during operation. It may be convenient to enclose the equationapparatus by side plates around the plates l2, l4 and 16, but in suchcase, these side plates should be made of transparent material for thereason of visibili- While particular embodiments of the presentinvention have been shown and described, it will be obvious to thoseskilled in the art that changes and modifications may be made withoutdeparting from this invention in its broader aspects and, therefore, theaim in the appended claims is to cover all such changes andmodifications as fall within the true spirit and scope of thisinvention.

What is claimed is:

1. An equation apparatus comprising:

first, second and third operating knobs;

first, second, and third number wheels having numbers thereon;

drive means coupling said operating knobs to respective said numberwheels in driving relationship thereto;

indicator means for indicating satisfaction of an equation; and

means interconnecting said operating knobs and said indicator means fordriving said indicator means from said operating knobs so that equationsatisfaction is indicated by said indicator means when said operatingknobs turn said number wheels so that such numbers on said number wheelsindicate satisfaction of an equation.

2. The equation apparatus of claim 1 wherein said drive means betweensaid operating knob and said number wheel is a one-way drive means.

3. The equation apparatus of claim 2 wherein said one-way drive meanscomprises a pawl in engagement with a ratchet wheel.

4. The equation apparatus of claim 3 wherein said pawl and ratchet wheelare arranged so that said operating knob turns said number wheel whensaid operating knob is turned in a clockwise direction.

5. The equation apparatus of claim 1 wherein said means interconnectingsaid operating knob and said indicator means includes a one-way drivemechanism.

6. The equation apparatus of claim 5 wherein said one-way drivemechanism is a pawl engaging a ratchet wheel.

7. The equation apparatus of claim 6 wherein said interconnecting meansincludes a plurality of pinions, each being connected to be driven byeach of said operating knobs, said pinions being geared together.

8. The equation apparatus of claim 7 wherein said drive means betweensaid operating knob and said number wheel is a one-way drive means.

9. The equation apparatus of claim 8 wherein said one-way drive meanscomprises a second pawl in engagement with a second ratchet wheel.

10. The equation apparatus of claim 9 wherein said second pawl andratchet wheel are arranged so that said operating knob turns said numberwheel when said operating knob is turned in a clockwise direction.

1 l. The equation apparatus of claim 1 wherein said meansinterconnecting said indicator means and said operating knobs comprisessecond drive means connected to each of said operating knobs to bedriven by said operating knobs.

12. The equation apparatus of claim 11 wherein said second drive meanscomprises a separate pinion driven by each of said operating knobs, saidseparate pinions being connected together in geartooth engagement.

13. The equation apparatus of claim 12 wherein the pinion driven by saidfirst operating knob is in engagement with a first idler and said firstidler is in engagement with said pinion driven by said second operatingknob, so that when one of said pinions is rotated, the other of saidpinions rotates in the same direction.

14. The equation apparatus of claim 13 wherein said pinion driven bysaid third operating knob is in engagement with a second idler, and saidsecond idler is in engagement with an indicator carrier gear, saidindicator carrier gear being in engagement with said second pinion sothat, when said first and second pinions rotate in one direction, saidthird pinion rotates in an opposite direction.

15. The equation apparatus of claim 14 wherein said indicator meanscomprises an indicator gear driven by said indicator carrier gear.

16. The equation apparatus of claim 15 wherein an indicator bar issecured to said indicator gear, said indicator bar showing when saidindicator gear indicates satisfaction of the equation.

17. The equation apparatus of claim 14 wherein said drive means betweensaid operating knob and said number wheel is a one-way drive means.

18. The equation apparatus of claim 17 wherein said one-way drive meanscomprises a pawl in engagement with a ratchet wheel.

19. The equation apparatus of claim 18 wherein said pawl and ratchetwheel are arranged so that said operating knob turns said number wheelwhen said operating knob is turned in a clockwise direction.

20. The equation apparatus of claim 14 wherein said second drive meansincludes a one-way drive mechanism.

21. The equation apparatus of claim 20 wherein said one-way drivemechanism is a pawl engaging a ratchet wheel.

22. The equation apparatus of claim 21 wherein said drive means betweensaid operating knob and said number wheel is a one-way drive means.

23. The equation apparatus of claim 22 wherein said one-way drive meanscomprises a second pawl in engagement with a second ratchet wheel.

24. The equation apparatus of claim 23 wherein said second pawl andratchet wheel are arranged so that said operating knob turns said numberwheel when said operating knob is turned in a clockwise direction.

25. The equation apparatus of claim 24 wherein said indicator meanscomprises an indicator gear driven by said indicator carrier gear.

26. The equation apparatus of claim 25 wherein an indicator bar issecured to said indicator gear, said indicator bar showing when saidindicator gear indicates satisfaction of the equation.

1. An equation apparatus comprising: first, second and third operatingknobs; first, second, and third number wheels having numbers thereon;drive means coupling said operating knobs to respective said numberwheels in driving relationship thereto; indicator means for indicatingsatisfaction of an equation; and means interconnecting said operatingknobs and said indicator means for driving said indicator means fromsaid operating knobs so that equation satisfaction is indicated by saidindicator means when said operating knobs turn said number wheels sothat such numbers on said number wheels indicate satisfaction of anequation.
 2. The equation apparatus of claim 1 wherein said drive meansbetween said operating knob and said number wheel is a one-way drivemeans.
 3. The equation apparatus of claim 2 wherein said one-way drivemeans comprises a pawl in engagement with a ratchet wheel.
 4. Theequation apparatus of claim 3 wherein said pawl and ratchet wheel arearranged so that said operating knob turns said number wheel when saidoperating knob is turned in a clockwise direction.
 5. The equationapparatus of claim 1 wherein said means interconnecting said operatingknob and said indicator means includes a one-way drive mechanism.
 6. Theequation apparatus of claim 5 wherein said one-way drive mechanism is apawl engaging a ratchet wheel.
 7. The equation apparatus of clAim 6wherein said interconnecting means includes a plurality of pinions, eachbeing connected to be driven by each of said operating knobs, saidpinions being geared together.
 8. The equation apparatus of claim 7wherein said drive means between said operating knob and said numberwheel is a one-way drive means.
 9. The equation apparatus of claim 8wherein said one-way drive means comprises a second pawl in engagementwith a second ratchet wheel.
 10. The equation apparatus of claim 9wherein said second pawl and ratchet wheel are arranged so that saidoperating knob turns said number wheel when said operating knob isturned in a clockwise direction.
 11. The equation apparatus of claim 1wherein said means interconnecting said indicator means and saidoperating knobs comprises second drive means connected to each of saidoperating knobs to be driven by said operating knobs.
 12. The equationapparatus of claim 11 wherein said second drive means comprises aseparate pinion driven by each of said operating knobs, said separatepinions being connected together in gear-tooth engagement.
 13. Theequation apparatus of claim 12 wherein the pinion driven by said firstoperating knob is in engagement with a first idler and said first idleris in engagement with said pinion driven by said second operating knob,so that when one of said pinions is rotated, the other of said pinionsrotates in the same direction.
 14. The equation apparatus of claim 13wherein said pinion driven by said third operating knob is in engagementwith a second idler, and said second idler is in engagement with anindicator carrier gear, said indicator carrier gear being in engagementwith said second pinion so that, when said first and second pinionsrotate in one direction, said third pinion rotates in an oppositedirection.
 15. The equation apparatus of claim 14 wherein said indicatormeans comprises an indicator gear driven by said indicator carrier gear.16. The equation apparatus of claim 15 wherein an indicator bar issecured to said indicator gear, said indicator bar showing when saidindicator gear indicates satisfaction of the equation.
 17. The equationapparatus of claim 14 wherein said drive means between said operatingknob and said number wheel is a one-way drive means.
 18. The equationapparatus of claim 17 wherein said one-way drive means comprises a pawlin engagement with a ratchet wheel.
 19. The equation apparatus of claim18 wherein said pawl and ratchet wheel are arranged so that saidoperating knob turns said number wheel when said operating knob isturned in a clockwise direction.
 20. The equation apparatus of claim 14wherein said second drive means includes a one-way drive mechanism. 21.The equation apparatus of claim 20 wherein said one-way drive mechanismis a pawl engaging a ratchet wheel.
 22. The equation apparatus of claim21 wherein said drive means between said operating knob and said numberwheel is a one-way drive means.
 23. The equation apparatus of claim 22wherein said one-way drive means comprises a second pawl in engagementwith a second ratchet wheel.
 24. The equation apparatus of claim 23wherein said second pawl and ratchet wheel are arranged so that saidoperating knob turns said number wheel when said operating knob isturned in a clockwise direction.
 25. The equation apparatus of claim 24wherein said indicator means comprises an indicator gear driven by saidindicator carrier gear.
 26. The equation apparatus of claim 25 whereinan indicator bar is secured to said indicator gear, said indicator barshowing when said indicator gear indicates satisfaction of the equation.